How to Design Programs Languages phần 2 ppt

Purpose: to compute e raised to a number
expt : (num num -> num)
Purpose: to compute the power of the first to the second number
floor : (real -> int)
Purpose: to determine the closest integer below a real number
gcd : (int int -> int)
Purpose: to compute the greatest common divisior
imag-part : (num -> real)
Purpose: to extract the imaginary part from a complex number
inexact->exact : (num -> num)
Purpose: to approximate an inexact number by an exact one
inexact? : (num -> boolean)
Purpose: to determine whether some number is inexact
integer->char : (int -> char)
Purpose: to lookup the character that corresponds to the given integer in the ASCII table (if
any)
integer? : (any -> boolean)
Purpose: to determine whether some value is an integer (exact or inexact)
lcm : (int int -> int)
Purpose: to compute the least common multiple of two integers
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log : (num -> num)
Purpose: to compute the base-e logarithm of a number
magnitude : (num -> real)
Purpose: to determine the magnitude of a complex number
make-polar : (real real -> num)
Purpose: to create a complex from a magnitude and angle
max : (real real -> real)
Purpose: to determine the largest number
min : (real real -> real)
Purpose: to determine the smallest number

modulo : (int int -> int)
Purpose: to compute first number modulo second number
negative? : (number -> boolean)
Purpose: to determine if some value is strictly smaller than zero
number->string : (num -> string)
Purpose: to convert a number to a string
number? : (any -> boolean)
Purpose: to determine whether some value is a number
numerator : (rat -> int)
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Purpose: to compute the numerator of a rational
odd? : (integer -> boolean)
Purpose: to determine if some value is odd or not
pi : real
Purpose: the ratio of a circle’s circumference to its diameter
positive? : (number -> boolean)
Purpose: to determine if some value is strictly larger than zero
quotient : (int int -> int)
Purpose: to compute the quotient of two integers
random : (int -> int)
Purpose: to generate a random natural number less than some given integer
rational? : (any -> boolean)
Purpose: to determine whether some value is a rational number
real-part : (num -> real)
Purpose: to extract the real part from a complex number
real? : (any -> boolean)
Purpose: to determine whether some value is a real number
remainder : (int int -> int)
Purpose: to compute the remainder of dividing the first by the second integer
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round : (real -> int)
Purpose: to round a real number to an integer (rounds to even to break ties)
sgn : (real -> (union 1 1.0 0 0.0 -1 -1.0))
Purpose: to compute the sign of a real number
sin : (num -> num)
Purpose: to compute the sine of a number (radians)
sinh : (num -> num)
Purpose: to compute the hyperbolic sine of a number
sqr : (num -> num)
Purpose: to compute the square of a number
sqrt : (num -> num)
Purpose: to compute the square root of a number
sub1 : (number -> number)
Purpose: to compute a number one smaller than a given number
tan : (num -> num)
Purpose: to compute the tangent of a number (radians)
zero? : (number -> boolean)
Purpose: to determine if some value is zero or not
boolean=? : (boolean boolean -> boolean)
Purpose: to determine whether two booleans are equal
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boolean? : (any -> boolean)
Purpose: to determine whether some value is a boolean
false? : (any -> boolean)
Purpose: to determine whether a value is false
not : (boolean -> boolean)
Purpose: to compute the negation of a boolean value
symbol->string : (symbol -> string)
Purpose: to convert a symbol to a string
symbol=? : (symbol symbol -> boolean)

Purpose: to determine whether two symbols are equal
symbol? : (any -> boolean)
Purpose: to determine whether some value is a symbol
append : ((listof any)
(listof any)
(listof any)

->
(listof any))
Purpose: to create a single list from several, by juxtaposition of the items
assq : (X
(listof (cons X Y))
->
(union false (cons X Y)))
Purpose: to determine whether some item is the first item of a pair in a list of pairs
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caaar : ((cons
(cons (cons W (listof Z)) (listof Y))
(listof X))
->
W)
Purpose: to select the first item of the first list in the first list of a list
caadr : ((cons
(cons (cons W (listof Z)) (listof Y))
(listof X))
->
(listof Z))
Purpose: to select the rest of the first list in the first list of a list
caar : ((cons (cons Z (listof Y)) (listof X)) -> Z)
Purpose: to select the first item of the first list in a list

cadar : ((cons (cons W (cons Z (listof Y))) (listof X))
->
Z)
Purpose: to select the second item of the first list of a list
cadddr : ((listof Y) -> Y)
Purpose: to select the fourth item of a non-empty list
caddr : ((cons W (cons Z (cons Y (listof X)))) -> Y)
Purpose: to select the third item of a non-empty list
cadr : ((cons Z (cons Y (listof X))) -> Y)
Purpose: to select the second item of a non-empty list
car : ((cons Y (listof X)) -> Y)
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Purpose: to select the first item of a non-empty list
cdaar : ((cons
(cons (cons W (listof Z)) (listof Y))
(listof X))
->
(listof Z))
Purpose: to select the rest of the first list in the first list of a list
cdadr : ((cons W (cons (cons Z (listof Y)) (listof X)))
->
(listof Y))
Purpose: to select the rest of the first list in the rest of a list
cdar : ((cons (cons Z (listof Y)) (listof X))
->
(listof Y))
Purpose: to select the rest of a non-empty list in a list
cddar : ((cons (cons W (cons Z (listof Y))) (listof X))
->
(listof Y))

Purpose: to select the rest of the rest of the first list of a list
cdddr : ((cons W (cons Z (cons Y (listof X))))
->
(listof X))
Purpose: to select the rest of the rest of the rest of a list
cddr : ((cons Z (cons Y (listof X))) -> (listof X))
Purpose: to select the rest of the rest of a list
cdr : ((cons Y (listof X)) -> (listof X))
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Purpose: to select the rest of a non-empty list
cons : (X (listof X) -> (listof X))
Purpose: to construct a list
cons? : (any -> boolean)
Purpose: to determine whether some value is a constructed list
eighth : ((listof Y) -> Y)
Purpose: to select the eighth item of a non-empty list
empty? : (any -> boolean)
Purpose: to determine whether some value is the empty list
fifth : ((listof Y) -> Y)
Purpose: to select the fifth item of a non-empty list
first : ((cons Y (listof X)) -> Y)
Purpose: to select the first item of a non-empty list
fourth : ((listof Y) -> Y)
Purpose: to select the fourth item of a non-empty list
length : (list -> number)
Purpose: to compute the number of items on a list
list : (any -> (listof any))
Purpose: to construct a list of its arguments
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list* : (any (listof any) -> (listof any))

Purpose: to construct a list by adding multiple items to a list
list-ref : ((listof X) natural-number -> X)
Purpose: to extract the indexed item from the list
member : (any list -> boolean)
Purpose: to determine whether some value is on the list (comparing values with equal?)
memq : (any list -> (union false list))
Purpose: to determine whether some value is on some list (comparing values with eq?)
memv : (any list -> (union false list))
Purpose: to determine whether some value is on the list (comparing values with eqv?)
null : empty
Purpose: the empty list
null? : (any -> boolean)
Purpose: to determine whether some value is the empty list
pair? : (any -> boolean)
Purpose: to determine whether some value is a constructed list
rest : ((cons Y (listof X)) -> (listof X))
Purpose: to select the rest of a non-empty list
reverse : (list -> list)
Purpose: to create a reversed version of a list
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second : ((cons Z (cons Y (listof X))) -> Y)
Purpose: to select the second item of a non-empty list
seventh : ((listof Y) -> Y)
Purpose: to select the seventh item of a non-empty list
sixth : ((listof Y) -> Y)
Purpose: to select the sixth item of a non-empty list
third : ((cons W (cons Z (cons Y (listof X)))) -> Y)
Purpose: to select the third item of a non-empty list
make-posn : (number number -> posn)
Purpose: to construct a posn

posn-x : (posn -> number)
Purpose: to extract the x component of a posn
posn-y : (posn -> number)
Purpose: to extract the y component of a posn
posn? : (anything -> boolean)
Purpose: to determine if its input is a posn
char->integer : (char -> integer)
Purpose: to lookup the number that corresponds to the given character in the ASCII table (if
any)
char-alphabetic? : (char -> boolean)
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Purpose: to determine whether a character represents an alphabetic character
char-ci<=? : (char char -> boolean)
Purpose: to determine whether a character precedes another (or is equal to it) in a case-
insensitive manner
char-ci<? : (char char -> boolean)
Purpose: to determine whether a character precedes another in a case-insensitive manner
char-ci=? : (char char -> boolean)
Purpose: to determine whether two characters are equal in a case-insensitive manner
char-ci>=? : (char char -> boolean)
Purpose: to determine whether a character succeeds another (or is equal to it) in a case-
insensitive manner
char-ci>? : (char char -> boolean)
Purpose: to determine whether a character succeeds another in a case-insensitive manner
char-downcase : (char -> char)
Purpose: to determine the equivalent lower-case character
char-lower-case? : (char -> boolean)
Purpose: to determine whether a character is a lower-case character
char-numeric? : (char -> boolean)
Purpose: to determine whether a character represents a digit

char-upcase : (char -> char)
Purpose: to determine the equivalent upper-case character
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char-upper-case? : (char -> boolean)
Purpose: to determine whether a character is an upper-case character
char-whitespace? : (char -> boolean)
Purpose: to determine whether a character represents space
char<=? : (char char -> boolean)
Purpose: to determine whether a character precedes another (or is equal to it)
char<? : (char char -> boolean)
Purpose: to determine whether a character precedes another
char=? : (char char -> boolean)
Purpose: to determine whether two characters are equal
char>=? : (char char -> boolean)
Purpose: to determine whether a character succeeds another (or is equal to it)
char>? : (char char -> boolean)
Purpose: to determine whether a character succeeds another
char? : (any -> boolean)
Purpose: to determine whether a value is a character
format : (string any -> string)
Purpose: to format a string, possibly embedding values
list->string : ((listof char) -> string)
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Purpose: to convert a s list of characters into a string
make-string : (nat char -> string)
Purpose: to produce a string of given length from a single given character
string : (char -> string)
Purpose: (string c1 c2 ) builds a string
string->list : (string -> (listof char))
Purpose: to convert a string into a list of characters

string->number : (string -> (union number false))
Purpose: to convert a string into a number, produce false if impossible
string->symbol : (string -> symbol)
Purpose: to convert a string into a symbol
string-append : (string -> string)
Purpose: to juxtapose the characters of several strings
string-ci<=? : (string string -> boolean)
Purpose: to determine whether one string alphabetically precedes another (or is equal to it)
in a case-insensitive manner
string-ci<? : (string string -> boolean)
Purpose: to determine whether one string alphabetically precedes another in a case-
insensitive manner
string-ci=? : (string string -> boolean)
Purpose: to compare two strings character-wise in a case-insensitive manner
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string-ci>=? : (string string -> boolean)
Purpose: to determine whether one string alphabetically succeeds another (or is equal to it)
in a case-insensitive manner
string-ci>? : (string string -> boolean)
Purpose: to determine whether one string alphabetically succeeds another in a case-
insensitive manner
string-copy : (string -> string)
Purpose: to copy a string
string-length : (string -> nat)
Purpose: to determine the length of a string
string-ref : (string nat -> char)
Purpose: to extract the i-the character from a string
string<=? : (string string -> boolean)
Purpose: to determine whether one string alphabetically precedes another (or is equal to it)
string<? : (string string -> boolean)

Purpose: to determine whether one string alphabetically precedes another
string=? : (string string -> boolean)
Purpose: to compare two strings character-wise
string>=? : (string string -> boolean)
Purpose: to determine whether one string alphabetically succeeds another (or is equal to it)
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string>? : (string string -> boolean)
Purpose: to determine whether one string alphabetically succeeds another
string? : (any -> boolean)
Purpose: to determine whether a value is a string
substring : (string nat nat -> string)
Purpose: to extract the substring starting at a 0-based index up to the second 0-based index
(exclusive)
image=? : (image image -> boolean)
Purpose: to determine whether two images are equal
image? : (any -> boolean)
Purpose: to determine whether a value is an image
=∼ : (real real non-negative-real -> boolean)
Purpose: to check whether two real numbers are within some amount (the third argument)
of either other
eof : eof
Purpose: the end-of-file value
eof-object? : (any -> boolean)
Purpose: to determine whether some value is the end-of-file value
eq? : (any any -> boolean)
Purpose: to compare two values
equal? : (any any -> boolean)
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Purpose: to determine whether two values are structurally equal
equal∼? : (any any non-negative-real -> boolean)

Purpose: to compare like equal? on the first two arguments, except using =∼ in the case of
real numbers
eqv? : (any any -> boolean)
Purpose: to compare two values
error : (symbol string -> void)
Purpose: to signal an error
exit : (-> void)
Purpose: to exit the running program
identity : (any -> any)
Purpose: to return the argument unchanged
struct? : (any -> boolean)
Purpose: to determine whether some value is a structure
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2 Beginning Student with List Abbreviations
program = def-or-expr
def-or-expr = definition
| expr
| test-case
| library-require
definition = (define (id id id ) expr )
| (define id expr )
| (define id (lambda (id id ) expr ))
| (define-struct id (id ))
expr = (id expr expr ) ; function call
| (prim-op expr ) ; primitive operation call
| (cond [expr expr ] [expr expr ])
| (cond [expr expr ] [else expr ])
| (if expr expr expr )
| (and expr expr expr )
| (or expr expr expr )

| empty
| id
| ’quoted ; quoted value
| ‘quasiquoted ; quasiquote
| number
| true
| false
| string
| character
quoted = id
| number
| string
| character
| (quoted )
| ’quoted
| ‘quoted
| ,quoted
| ,@quoted
quasiquoted = id
| number
| string
| character
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